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Abstract

An application of the Green’s function method to the
one-dimensional radiative transfer problem with a non-Lambertian
surface is described. This method separates atmospheric radiative
transport from the lower boundary condition and allows expressing a
solution analytically for an arbitrary surface reflectance. In the
physical sense, the Green’s function represents bidirectional
atmospheric transmission for the unitary radiance source located at the
bottom of the atmosphere. The boundary-value problem for the
Green’s function is adjoint to the problem for atmospheric path
radiance, and therefore it can be solved by use of existing numerical
methods by reversal of the direction of light propagation. From an
analysis of an exact operator solution and extensive numerical study,
we found two accelerating parameterizations for computing the
surface-reflected radiance. The first one is a maximum-eigenvalue
method that is comparable in accuracy with rigorous radiative transfer
codes in calculations with realistic land-cover types. It requires
a total of the first three orders of the surface-reflected
radiance. The second one is based on the Lambertian approximation
of multiple reflections. Designed for operational applications, it
is much faster: Already the first-order reflected radiance ensures
an average accuracy of better than 1%.

References

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